"As we leave the European Union we will forge a bold new positive role for ourselves in the world, and we will make Britain a country that works not for a privileged few, but for every one of us."

Brussels welcomes appointment of May as British PM

But May also told EU leaders that she needed time to carry out the British exit, or Brexit.

In phone conversations with the leaders of Germany, France and Ireland, who called to wish her well as Britain's second-ever woman prime minister, May underlined her commitment to a British exit, or Brexit.

"On all the phone calls, the prime minister emphasised her commitment to delivering the will of the British people to leave the European Union," a spokeswoman for May said, according to a Reuters news agency report.

"The prime minister explained that we would need some time to prepare for these negotiations and spoke of her hope that these could be conducted in a constructive and positive spirit," the spokeswoman said.

"The outcome of the United Kingdom’s referendum has created a new situation which the United Kingdom and the European Union will have to address soon," Juncker said in a letter published on his Twitter account.

"I look forward to working closely with you on this and to learn about your intentions in this regard," he said.

His comments were echoed by European Parliament President Martin Schulz.

"Leadership issue settled, now I expect we work quickly to deliver certainty," he said.

Belgian Prime Minister Charles Michel added his voice to those pleading for a speedy start to the Brexit procedure, following three weeks of financial and political turmoil triggered by Britain’s vote to leave Europe.

"We can't afford a long period of uncertainty," he said.

German Chancellor Angela Merkel said on Thursday that she spoke to May by phone late on Wednesday and invited her for talks in Berlin.

"It's our task to work very closely with governments of ally countries," Merkel told a news conference in Bishkek, Kyrgyzstan, adding there were many problems in the world that made such close cooperation necessary.

"I look forward to working together," she said.

The German Chancellor declined to comment on May's decision to appoint former London Mayor Boris Johnson - who led the Leave campaign ­- as her new foreign minister.

Minister Boris

By awarding such a senior job to Johnson, analysts say May is trying to mend fences inside her party, which was ripped apart by the Brexit vote, and forced former Conservative Party leader David Cameron to resign as prime minister, making way for May's rise.

May herself had sided with Cameron in trying to keep Britain inside the EU, so she now needs to reach out to the winning "Leave" side in order to heal divisions and show her commitment to respecting the popular vote.

Since the vote to leave the EU, Johnson has suffered widespread criticism and ridicule for failing to present a clear Brexit plan and swiftly dropping out of the prime ministerial race.

Other prominent "Leave" campaigners were also rewarded by May, including David Davis, who took the key role of Secretary of State for Exiting the European Union. Another, Liam Fox, was named to head a new international trade department.